A mathematical model for the activated sludge process with a sludge disintegration unit

We develop and investigate a model for sludge production in the activated sludge process when a biological reactor is coupled to a sludge disintegration unit (SDU). The model for the biological reactor is a slimmed down version of the activated sludge model 1 in which only processes related to carbon are retained. Consequently, the death-regeneration concept is included in our model which is an improvement on almost all previous models. This provides an improved representation of the total suspended solids in the biological reactor, which is the key parameter of interest. We investigate the steady-state behaviour of this system as a function of the residence time within the biological reactor and as a function of parameters associated with the operation of the SDU. A key parameter is the sludge disintegration factor. As this parameter is increased the concentration of total suspended solids within the biological reactor decreases at the expense increasing the chemical oxygen demand in the effluent stream. The existence of a maximum acceptable chemical oxygen demand in the effluent stream therefore imposes a maximum achievable reduction in the total suspended solids. This paper improves our theoretical understanding of the utility of sludge disintegration as a means to reduce excess sludge formation. As an aside to the main thrust of our paper we investigate the common assumption that the sludge disintegration processes occur on a much shorter timescale than the biological processes. We show that the disintegration processes must be exceptional slow before the inclusion of the biological processes becomes important.